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The Lebesgue function for generalized Hermite-Fejér interpolation on the Chebyshev nodes

Published online by Cambridge University Press:  17 February 2009

Graeme J. Byrne ,
T. M. Mills  and
Simon J. Smith
Graeme J. Byrne
Affiliation:
Division of Mathematics, La Trobe University, P.O. Box 199, Bendigo, VIC 3552, Australia.
T. M. Mills
Affiliation:
Division of Mathematics, La Trobe University, P.O. Box 199, Bendigo, VIC 3552, Australia.
Simon J. Smith
Affiliation:
Division of Mathematics, La Trobe University, P.O. Box 199, Bendigo, VIC 3552, Australia.
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Abstract

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This paper presents a short survey of convergence results and properties of the Lebesgue function λm,n(x) for(0, 1, …, m)Hermite-Fejér interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n → ∞ of the Lebesgue constant Λm,n = max{λm,n(x): −1 ≤ x ≤ 1} for even m is then studied, and new results are obtained for the asymptotic expansion of Λm,n. Finally, graphical evidence is provided of an interesting and unexpected pattern in the distribution of the local maximum values of λm,n(x) if m ≥ 2 is even.

Type
Research Article
Information
The ANZIAM Journal , Volume 42 , Issue 1 , July 2000 , pp. 98 - 109
Copyright
Copyright © Australian Mathematical Society 2000

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